$\dfrac{1 - \cos^2\theta}{\sec^2\theta} = \; ?$
Solution: We can use the identity ${\sin^2 \theta} + {\cos^2 \theta} = 1$ to simplify this expression. $1$ ${\sin\theta}$ ${\cos\theta}$ $\theta$ We can see why this is true by using the Pythagorean Theorem. So, $1 - \cos^2\theta = \sin^2\theta$ Plugging into our expression, we get $ \dfrac{1 - \cos^2\theta}{\sec^2\theta} = \dfrac{\sin^2\theta}{\sec^2\theta} $ To make simplifying easier, let's put everything in terms of $\sin$ and $\cos$ $\sec^2\theta = \frac{1}{\cos^2\theta}$ , so we can plug that in to get $ \dfrac{\sin^2\theta}{\sec^2\theta} = \dfrac{\sin^2\theta}{\frac{1}{\cos^2\theta}} $ This is $\cos^2\theta \cdot \sin^2\theta$.